Gradient based iterative parameter identification for Wiener nonlinear systems

This paper focuses on the identification problem of Wiener nonlinear output error systems. The application of the key-term decomposition technique provides a special form of the Wiener model with polynomials, where all the model parameters to be estimated are separated. To solve the identification problem of Wiener nonlinear output error systems with the unmeasurable variables in the information vector, an auxiliary model-based gradient iterative algorithm is presented by replacing the unmeasurable variables with their corresponding iterative estimates. The performances of the proposed algorithm are analyzed and compared by using numerical examples.     

HOLDER ESTIMATES FOR A CLASS OF DEGENERATE ELLIPTIC EQUATIONS

In this paper we study the regularity theory of the solutions of a class of degenerate elliptic equations in divergence form. By introducing a proper distance and applying the compactness method we establish the HSlder type estimates for the weak solutions.     

The quasiderivative method for derivative estimates of solutions to degenerate elliptic equations

We give an example of quasiderivatives constructed by random time change, Girsanov’s Theorem and Levy’s Theorem. As an application, we investigate the smoothness and estimate the derivatives up to second order for the probabilistic solution to the Dirichlet problem for the linear degenerate elliptic partial differential equation of second order, under the assumption of non-degeneracy with respect to the normal to the boundary and an interior condition to control the moments of quasiderivatives, which is weaker than non-degeneracy.     

On strong solutions of a Robin problem modelling heat conduction in materials with corroded boundary

Motivated by a practical problem on a corrosion process, we shall study a third kind of BVP for a large class of elliptic equations in vector-valued L_p spaces. Particularly we will determine optimal spaces for boundary data and get maximal regularity for inhomogeneous equations. Then based on these results we shall treat some nonlinear problems. Our approach will be based on the semigroup theory, the interpolation theory of Banach spaces, fractional powers of positive operators, operator-valued Fourier multiplier theorems and the Banach fixed point theorem.     

Global classical solutions of coagulation-fragmentation equations with unbounded coagulation rates

We study discrete fragmentation coagulation equations in spaces X_p, p>1, consisting of distributions having the pth moments finite. We show that for sufficiently regular fragmentation laws the fragmentation semigroup is analytic in X_p, and fully characterize the domain of its generator. This allows for explicit characterization of the domains of the fractional powers of the generator through real interpolation. Finally, we use the linear results to show the existence of global classical solutions to fragmentation coagulation equations for a class of unbounded coagulation kernels.     

非线性渗流耦合系统动边值问题二阶迎风分数步差分方法

对多层非线性渗流方程耦合系统三维动边值问题, 提出适合并行计算的一类二阶迎风分数步差分格式, 利用区域变换、变分形式、能量方法、隐显格式的相互结合、差分算子乘积交换性、高阶差分算子的分解、先验估计的理论和技巧, 得到收敛性的最佳阶l² 误差估计. 该方法已成功地应用到多层油资源运移聚集的资源评估生产实际中, 得到了很好的数值模拟结果.     

Crystal growth and spectral properties of Nd:Ca5(BO3)3F

A neodymium doped Ca₅(BO₃)₃F single crystal with size up to 51×48×8 mm³ has been grown by the top seeded solution growth (TSSG) technique with a Li₂O‐B₂O₃‐LiF flux. The spectra of absorption and fluorescence were measured at room temperature. According to Judd‐Ofelt (J‐O) theory, the spectroscopic parameters were calculated and the J‐O parameters Ω₂, Ω₄, Ω₆ were obtained as follows: Ω₂ = 1.41×10⁻²⁰cm², Ω₄ = 3.18×10⁻²⁰cm², Ω₆ = 2.11×10⁻²⁰cm². The room temperature fluorescence lifetime of NCBF was measured to be 51.8 μs. According to the J‐O paramenters, the emission probabilities of transitions, branching ratios, the radiative lifetime and the quantum efficiency from the Nd^{3+ 4}F_3/2 metastable state to lower lying J manifolds were also obtained. In comparasion with other Nd‐doped borate crystals, the calculated and experimental parameters show that NCBF is a promising SFD crystal.     

Large time behavior of differential equations with drifted periodic coefficients modeling carbon storage in soil

This paper is concerned with the linear ODE in the form y′(t) = λρ(t)y(t) + b(t), λ < 0 which represents a simplified storage model of the carbon in the soil. In the first part, we show that, for a periodic function ρ(t), a linear drift in the coefficient b(t) involves a linear drift for the solution of this ODE. In the second part, we extend the previous results to a classical heat non-homogeneous equation. The connection with an analytic semi-group associated to the ODE equation is considered in the third part. Numerical examples are given.